Appendix A: The Derivation of Unit Costs and the Relevance of Particular Discount Rates and Unit Costs for Different Types of Analysis
A.1 National Cost Benefit Analysis
In national cost benefit analyses, it can be useful to assess the c/kWh unit costs of different proposed or possible new sources of generation.
The fuel and variable O&M costs are readily expressed in c/kWh terms and these costs are relatively unambiguous whatever the utilisation pattern of the plant; whether the plant is base loaded or used only occasionally, the same unit costs apply.
A.1.1 Estimating Unit Capital Costs
The conversion of capital costs and fixed O&M costs into c/kWh terms requires two steps:
- annuitising the capital costs into equivalent annual costs and adding the annual fixed O&M costs (this is sometimes called levelising the costs), and
- spreading the total of these annual costs over the number of units to be generated in a year.
The annuity is the annual payment that will recover the capital cost of the plant over a specified project life and earn a given rate of return in the process. Expressed differently, the present value of the annuity stream equals the (present value of) capital costs.
The annuitisation of capital costs can be derived using the normal formula that requires that the present value of payments equals the capital cost:
C = C.PMT[1/(1 + R) + … + 1/(1 + R)L ]
where:
C = the up front capital cost
PMT = a proportional annuity factor,2 defined so that C.PMT is the equivalent annual payment to be derived
R = the real public sector discount rate, which is currently assumed to be 10%,
and
L = the expected life of the investment in years.
Note that the annuity factor is just:
PMT = 1/[1/(1 + R) + … + 1/(1 + R)L ] = R/[1 - (1 + R)-L ].
Conversion of the equivalent annual costs into c/kWh unit costs depends on load factors. In this report, 90% load factors are used in the base case, but results are also given for 60% load factors.
A.1.2 Construction and Commissioning Periods
Various technologies require differing times for construction and this can spread over several years, during which time capital costs are incurred. Generally civil costs are incurred at an early stage in the project and the mechanical and electrical costs in the latter stages. The modelling of capital costs for this report uses annual steps, and the capital expenditure for coal plant has been spread over three years, combined cycle gas turbines two years, and open cycle combustion turbines one year.
Commissioning (ramping up to full GWh capability) can be also be spread over a period, in some cases up to 12 months or more, particularly with multiple units or staged construction. In the cases considered here, because they are single units, generation build up is assumed to take place over one quarter of the commissioning year except for coal plant when generation build up is over two quarters.
A.1.3 What Cost Estimates to Use in a National Cost Benefit Analysis?
All the unit cost estimates in this report are in real (not nominal) terms.
In a national cost benefit analysis (cba) it would be appropriate to use the c/kWh capital, fuel and O&M costs (but not tax costs) that are provided for a 10% discount rate.
A.2 Commercial Analysis
In New Zealand, investments in generating plant do not proceed on the basis of national cost benefit analyses. Decisions on whether or not to invest are made on a commercial basis. Accordingly, in assessing what plants are likely to be built and in which order (assuming lower cost options are built first), commercial criteria should be applied. Note that the total unit cost of a plant indicates the market price of electricity that would be required for the plant to be economic.
A.2.1 Estimating Unit Capital Costs
In a commercial setting, the investor requires that the present value (at a competitive investor's Weighted Average Cost of Capital (WACC)) of the post-tax cash flow arising from the annual payments equals at least the up front capital cost. (The investor may also consider that there are risks that are not allowed for by the WACC, and therefore seek a premium on the WACC.) The unit cost derived from the annual payment figure is then the price that would earn the investor a competitive rate of return, post-tax.
Compared with a national cost benefit analysis, there are two differences:
- instead of using the public sector discount rate it is necessary to use the investor's post-tax WACC, and
- it is necessary to provide for the fact that the returns that the investor receives will be net of tax. In a national cost benefit analysis it is assumed that tax does not constitute a loss but rather a re-distribution of income from one person to another, and as a result it is not necessary to take it into account.
It is not easy to assess the competitive investor's post-tax WACC in New Zealand. However, it is considered that a real (not nominal) post-tax WACC of 7.5% is a reasonable figure. For this reason, a discount rate of 7.5% has been chosen as the base case rate in this report.
Turning to the issue of tax, in a commercial analysis the annuitisation of capital costs requires two tax effects to be taken into account:
- the basic payment of corporate tax, which tends to increase unit costs required in order for the investor to obtain an adequate post-tax return, and
- depreciation allowances that help moderate the amount of tax that has to be paid.
Where the tax rate is t (assumed to be 33%), the basic tax effect increases the size of the annual payments required to achieve an adequate return by a factor of 1/(1 - t).
With straight line depreciation, the amount of tax that depreciation saves each year is t.C/L. This amount is commonly referred to as the depreciation tax shield. It is possible to calculate the present value worth of the shield by using an annuity factor. The annuity factor has the same form as that described in 0, but in this case because tax has to be paid and the shield operates on nominal (not real) income, the relevant annuity factor is that for the post-tax nominal WACC; call it PMT'. Then the present value of the shield is t.C/(L.PMT'), and this effectively reduces the up front capital cost from C to C(1 - t/(L.PMT')).
In preparing this report it has been assumed that inflation is 2% pa. Accordingly, this has been taken into account in preparing nominal income figures, and nominal WACCs. For example, the post-tax nominal WACC corresponding with the post-tax real WACC of 7.5% is (1.02 x 1.075 - 1) = 9.7%.
It is now necessary to annuitise this capital cost and also take into account the 1/(1 - t) tax factor. Here it is normal to calculate the equivalent annual payments in real terms since it is assumed that the ultimate price calculated keeps up with inflation. Accordingly, the relevant annuity factor in this case is that for the investor's post-tax real WACC. (Note this is not the same PMT as in Part 1; there the PMT was that for the public sector discount rate.) The resulting annuitised capital cost is then given by:
PMT.C(1 - t/(L.PMT'))/(1 - t) = C.PMT + t.C.PMT(1 - 1/(L.PMT'))/(1 - t).
The first component of the last expression (C.PMT) corresponds to the annuitised capital costs given in this report, while the second component corresponds to the annuitised tax costs. The capital and tax c/kWh unit costs have been derived from such components.
The treatment above is a simplified approach that assumes a single representative life for all assets and straight line depreciation. The capital and tax unit costs given in the body of the report have been calculated after taking into account a number of factors such as construction and commissioning periods (see below).
As mentioned in A.1.1, the load factors have to be taken into account in converting equivalent annual costs into unit costs.
A.2.2 Construction and Commissioning Periods
As outlined in A.1.2, the effects of these periods extending over several quarters or years have been taken into account in preparing the unit capital unit costs. The capital unit cost estimates can be used in either a national cost benefit analysis or a commercial analysis (providing the appropriate discount rate is chosen). Tax costs need to be included in a commercial analysis. Since tax costs are driven off capital costs, the effects of construction and commissioning periods are also built into their estimation.
A.2.3 What Cost Estimates to Use in a Commercial Analysis?
In a commercial analysis it would be appropriate to use the c/kWh capital, fuel, O&M and tax costs given in this report. As mentioned above, it is somewhat difficult to know what discount rate to use. It is suggested that, unless there is specific evidence for using a different rate, the 7.5% base case rate of the report be used. This should be interpreted as a post-tax real WACC.
In A.1.3 it was suggested that the unit cost estimates given in the report for capital, fuel and O&M costs for a 10% discount rate would be appropriate to use in a national cost benefit analysis (cba). A question that might be posed is how this is the case when the commercial analysis involves tax effects that are not relevant in a cba.
The reason is as follows. With respect to unit capital costs, the effect of tax is separated out into the unit tax cost which should not be included in a cba. With respect to fuel and O&M unit costs, tax does no affect these. In a commercial context an investor would gain the tax benefit of expensing cost such that the effective cost was actual expenditure factored down by (1 - t). But then in order for the investor to gain an adequate rate of return post-tax the income received has to be the effective cost factored up 1/(1 - t). Thus the net tax effect is zero, and the relevant unit cost in a commercial analysis is equal to the actual unit cost, the same unit cost as relevant in a cba. Although, as noted elsewhere, different discount rates are likely to be appropriate in the two types of analysis.
Another question is whether the cost estimates given in this report are directly comparable to those given elsewhere, for example in the UK report cited in the bibliography, The Cost of Generating Electricity. Clearly circumstances in the UK differ from those in NZ. Also, it is not entirely clear on what basis the UK report has been prepared. It uses a nominal discount rate of 7.5%, and this suggests that it is a commercial analysis, but there does not appear to be any reference to tax so this may not be the case. Caution should be exercised in comparing results from different sources, especially where all the assumptions are not fully specified.
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